It is also of importance to discuss how the gap- and wave-function lengths can be extracted from the numerical solution of the BdG equations for an isolated vortex. There are different practical definitions of \(\xi _{\Delta }\)  utilized in the single-band case. It can be defined as the size of the vortex core related to the gap function slope [1]}, [2]}, [3]}, [4]}, or the radius of the maximal supercurrent density [5]}, or the radius of a cylinder containing the energy equal to the condensation energy [6]}, [7]}. One can also identify \(\xi _{\Delta }\)  as the healing length, i.e. the distance over which the gap function can nearly heal, being suppressed in the center of a vortex. In the latter case \(\xi _{\Delta }\)  can be found from the fact that the radial profile of the gap function is well approximated [3]}, [4]} as \(\Delta (\rho )=\Delta _0\rho /\sqrt{\rho ^2 + \xi ^2_{\Delta }}\) , with \(\Delta _0\)  the bulk value of the gap function.
